\u0939\u0932 :\u00a0<\/strong><\/p>\n<\/p>\n
\u0926\u094b \u0938\u0902\u0915\u0947\u0902\u0926\u094d\u0930\u0940 \u0935\u0943\u0924\u094d\u0924 \u091c\u093f\u0938\u0915\u093e \u0915\u0947\u0902\u0926\u094d\u0930 O \u0939\u0948 \u0914\u0930 \u092c\u095c\u0947 \u0935\u0943\u0924\u094d\u0924 \u0915\u0940<\/p>\n
\u091c\u0940\u0935\u093e AB \u0939\u0948 \u091c\u094b \u091b\u094b\u091f\u0947 \u0935\u0943\u0924\u094d\u0924 \u0915\u094b \u092c\u093f\u0902\u0926\u0941 M \u092a\u0930 \u092a\u094d\u0930\u0924\u093f\u091a\u094d\u091b\u0947\u0926 \u0915\u0930\u0924\u0940 \u0939\u0948 |<\/p>\n
\u0924\u094d\u0930\u093f\u091c\u094d\u092f\u093e\u090f\u0901 \u0915\u094d\u0930\u092e\u0936: AO = 5 cm \u0914\u0930 OM = 3 cm \u0939\u0948 |<\/p>\n
OM \u22a5 AB \u0939\u0948 | (\u091a\u0942\u0901\u0915\u093f \u091c\u0940\u0935\u093e \u0915\u094b \u0915\u0947\u0902\u0926\u094d\u0930 \u0938\u0947 \u092e\u093f\u0932\u093e\u0928\u0947 \u0935\u093e\u0932\u0940 \u0930\u0947\u0916\u093e\u0916\u0923\u094d\u0921 \u091c\u0940\u0935\u093e \u092a\u0930 \u0932\u0902\u092c \u0939\u094b\u0924\u0940 \u0939\u0948 |)<\/p>\n
\u0905\u0924: \u0938\u092e\u0915\u094b\u0923 \u0924\u094d\u0930\u093f\u092d\u0941\u091c AOM \u092e\u0947\u0902, \u092a\u093e\u0907\u0925\u093e\u0917\u094b\u0930\u0938 \u092a\u094d\u0930\u092e\u0947\u092f \u0938\u0947,<\/p>\n
OA2<\/sup>\u00a0= OM2<\/sup>\u00a0+ AM2<\/sup><\/p>\n52<\/sup>\u00a0= 32<\/sup>\u00a0+ AM2<\/sup><\/p>\n52<\/sup>\u00a0– 32<\/sup>\u00a0= AM2<\/sup><\/p>\n25 – 9 = AM2<\/sup><\/p>\nAM2<\/sup>\u00a0= 16<\/p>\nAM = \u00a0= 4 cm<\/p>\n
\u0905\u0924: AB = 2 \u00d7 AM<\/p>\n
= 2 \u00d7 4 = 8 cm<\/p>\n
\u091c\u0940\u0935\u093e \u0915\u0940 \u0932\u0902\u092c\u093e\u0908 8 cm \u0939\u0948 |<\/p>\n
Ex 10.2 Class 10 \u0917\u0923\u093f\u0924\u00a0Q8. \u090f\u0915 \u0935\u0943\u0924\u094d\u0924 \u0915\u0947 \u092a\u0930\u093f\u0917\u0924 \u090f\u0915 \u091a\u0924\u0941\u0930\u094d\u092d\u091c ABCD \u0916\u0940\u0902\u091a\u093e \u0917\u092f\u093e \u0939\u0948 (\u0926\u0947\u0916\u093f\u090f \u0906\u0915\u0943\u0924\u093f 10.12 ) | \u0938\u093f\u0926\u094d\u0927 \u0915\u0940\u091c\u093f\u090f : AB + CD = AD + BC. \u00a0\u00a0 \u00a0<\/strong><\/p>\n\u0939\u0932 :<\/strong><\/p>\n\u0926\u093f\u092f\u093e \u0939\u0948 :<\/strong>\u00a0ABCD \u090f\u0915 O \u0915\u0947\u0902\u0926\u094d\u0930 \u0935\u093e\u0932\u0947 \u0935\u0943\u0924\u094d\u0924 \u0915\u0947 \u092a\u0930\u093f\u0917\u0924 \u092c\u0928\u093e \u091a\u0924\u0941\u0930\u094d\u092d\u0941\u091c \u0939\u0948 | \u0930\u0947\u0916\u093e\u090f\u0901 AB, BC, CD \u0914\u0930 AD \u0915\u094d\u0930\u092e\u0936: \u092c\u093f\u0902\u0926\u0941 P, Q, R \u0914\u0930 S \u092a\u0930 \u0938\u094d\u092a\u0930\u094d\u0936 \u0915\u0930\u0924\u0940 \u0939\u0948\u0902 |<\/p>\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :<\/strong>\u00a0AB + CD = AD + BC<\/p>\n<\/p>\n
\u092a\u094d\u0930\u092e\u093e\u0923 :<\/strong>\u00a0P \u0914\u0930 S \u0938\u094d\u092a\u0930\u094d\u0936 \u092c\u093f\u0902\u0926\u0941 \u0939\u0948\u0902 |<\/p>\n\u0905\u0924: AP = AS\u00a0\u00a0 …………… (i)\u00a0\u00a0 \u092a\u094d\u0930\u092e\u0947\u092f 10.2 \u0938\u0947<\/p>\n
(\u092c\u093e\u0939\u094d\u092f \u092c\u093f\u0902\u0926\u0941 \u0938\u0947 \u0916\u093f\u0902\u091a\u0940 \u0917\u0908 \u0938\u094d\u092a\u0930\u094d\u0936 \u0930\u0947\u0916\u093e\u090f\u0901 \u0938\u092e\u093e\u0928 \u0932\u0902\u092c\u093e\u0908 \u0915\u0940 \u0939\u094b\u0924\u0940 \u0939\u0948 |)<\/p>\n
\u0907\u0938\u0940\u092a\u094d\u0930\u0915\u093e\u0930,<\/p>\n
BP = BQ\u00a0\u00a0 …………… (ii)<\/p>\n
CR = CQ\u00a0\u00a0 …………… (iii)<\/p>\n
\u0914\u0930 DR = DS\u00a0\u00a0\u00a0 …………… (iv)<\/p>\n
\u0938\u092e\u0940\u0966 (i), (ii), (iii) \u0914\u0930 (iv) \u091c\u094b\u095c\u0928\u0947 \u092a\u0930<\/p>\n
AP + BP + CR + DR = AS + DS + BQ + CQ<\/p>\n
AB + CD = AD + BC\u00a0Proved<\/strong><\/p>\nEx 10.2 Class 10 \u0917\u0923\u093f\u0924\u00a0Q9. \u0906\u0915\u0943\u0924\u093f 10.13 \u092e\u0947\u0902 XY \u0924\u0925\u093e X’Y’, O \u0915\u0947\u0902\u0926\u094d\u0930 \u0935\u093e\u0932\u0947 \u0915\u093f\u0938\u0940 \u0935\u0943\u0924\u094d\u0924 \u092a\u0930 \u0926\u094b \u0938\u092e\u093e\u0902\u0924\u0930 \u0938\u094d\u092a\u0930\u094d\u0936 \u0930\u0947\u0916\u093e\u090f\u0901 \u0939\u0948\u0902 \u0914\u0930 \u0938\u094d\u092a\u0930\u094d\u0936 \u092c\u093f\u0928\u094d\u0926\u0941 C \u092a\u0930 \u0938\u094d\u092a\u0930\u094d\u0936 \u0930\u0947\u0916\u093e AB, XY \u0915\u094b A \u0924\u0925\u093e X’Y’ \u0915\u094b B \u092a\u0930 \u092a\u094d\u0930\u0924\u093f\u091a\u094d\u091b\u0947\u0926 \u0915\u0930\u0924\u0940 \u0939\u0948 | \u0938\u093f\u0926\u094d\u0927 \u0915\u0940\u091c\u093f\u090f \u0915\u0940\u00a0\u2220AOB = 90o\u00a0<\/sup>\u0939\u0948 |<\/strong><\/p>\n\u0939\u0932 :<\/strong><\/p>\n\u0926\u093f\u092f\u093e \u0939\u0948 :<\/strong>\u00a0XY \u0924\u0925\u093e X’Y’, O \u0915\u0947\u0902\u0926\u094d\u0930 \u0935\u093e\u0932\u0947 \u0915\u093f\u0938\u0940 \u0935\u0943\u0924\u094d\u0924 \u092a\u0930 \u0926\u094b \u0938\u092e\u093e\u0902\u0924\u0930 \u0938\u094d\u092a\u0930\u094d\u0936 \u0930\u0947\u0916\u093e\u090f\u0901 \u0939\u0948\u0902 \u0914\u0930 \u0938\u094d\u092a\u0930\u094d\u0936 \u092c\u093f\u0928\u094d\u0926\u0941 C \u092a\u0930 \u0938\u094d\u092a\u0930\u094d\u0936 \u0930\u0947\u0916\u093e AB, XY \u0915\u094b A \u0924\u0925\u093e X’Y’ \u0915\u094b B \u092a\u0930 \u092a\u094d\u0930\u0924\u093f\u091a\u094d\u091b\u0947\u0926 \u0915\u0930\u0924\u0940 \u0939\u0948 |<\/p>\n\u0938\u093f\u0926\u094d\u0927 \u0915\u0930\u0928\u093e \u0939\u0948 :<\/strong>\u00a0\u2220AOB = 90o\u00a0<\/sup><\/p>\n\u092a\u094d\u0930\u092e\u093e\u0923 :\u00a0<\/strong><\/p>\n<\/p>\n
\u2206AOP \u0914\u0930\u00a0\u2206AOC \u092e\u0947\u0902<\/p>\n
PA =\u00a0CA\u00a0\u00a0\u00a0 (\u092d\u0941\u091c\u093e) \u092a\u094d\u0930\u092e\u0947\u092f 10.2 \u0938\u0947<\/p>\n
\u2220APO =\u00a0\u2220ACO\u00a0\u00a0 90\u0966\u00a0<\/sup>\u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915<\/p>\nAO = AO\u00a0\u00a0\u00a0\u00a0 \u0909\u092d\u092f\u0928\u093f\u0937\u094d\u0920 \u0915\u0930\u094d\u0923<\/p>\n
RHS \u0938\u0930\u094d\u0935\u093e\u0902\u0917\u0938\u092e\u0924\u093e \u0928\u093f\u092f\u092e \u0938\u0947<\/p>\n
\u2206AOP \u2245 \u2206AOC<\/p>\n
\u0907\u0938\u0932\u093f\u090f,\u00a0\u2220PAO =\u00a0\u2220CAO\u00a0\u00a0 (i) BY CPCT<\/p>\n
\u2206BOQ \u2245 \u2206BOC<\/p>\n
\u0907\u0938\u0932\u093f\u090f,\u00a0\u2220QBO =\u00a0\u2220CBO\u00a0\u00a0 (ii) BY CPCT<\/p>\n
\u0905\u092c XY ||\u00a0X’Y’ \u0926\u093f\u092f\u093e \u0939\u0948 |<\/p>\n
\u0907\u0938\u0932\u093f\u090f,\u00a0\u2220PAC +\u00a0\u2220QBC = 180\u0966<\/sup>\u00a0 (\u0924\u093f\u0930\u094d\u092f\u0915 \u0930\u0947\u0916\u093e \u0915\u0947 \u090f\u0915 \u0939\u0940 \u0913\u0930 \u0915\u0947 \u0905\u0902\u0924:\u0915\u094b\u0923\u094b\u0902 \u0915\u093e \u092f\u094b\u0917 )<\/p>\n\u092f\u093e\u00a0\u00a0 (\u2220PAO +\u00a0\u2220CAO) + (\u2220QBO +\u00a0\u2220CBO) = 180\u0966<\/sup><\/p>\n\u092f\u093e\u00a0\u00a0 (\u2220CAO +\u00a0\u2220CAO) + (\u2220CBO +\u00a0\u2220CBO) = 180\u0966<\/sup>\u00a0\u00a0 (\u0938\u092e\u0940\u0966 (i) \u0924\u0925\u093e (ii) \u0915\u0947 \u092a\u094d\u0930\u092f\u094b\u0917 \u0938\u0947 )<\/p>\n\u092f\u093e\u00a0\u00a0 2\u00a0\u2220CAO + 2\u00a0\u2220CBO = 180\u0966<\/sup><\/p>\n\u092f\u093e\u00a0\u00a0 2 (\u2220CAO +\u00a0\u2220CBO) = 180\u0966<\/sup><\/p>\n<\/p>\n
\u092f\u093e\u00a0\u00a0\u2220CAO +\u00a0\u2220CBO = 90\u0966<\/sup>\u00a0\u00a0\u00a0 ………….. (iii)<\/p>\n\u0905\u092c \u0924\u094d\u0930\u093f\u092d\u0941\u091c AOB \u092e\u0947\u0902,<\/p>\n
\u2220AOB +\u00a0\u2220CAO +\u00a0\u2220CBO = 180\u0966<\/sup><\/p>\n\u2220AOB + 90\u0966<\/sup>\u00a0= 180\u0966<\/sup><\/p>\n\u2220AOB = 180\u0966<\/sup>\u00a0– 90\u0966<\/sup><\/p>\n\u2220AOB = 90\u0966<\/sup>\u00a0\u00a0