Two figures are givenIn fig i PQ is a tangent to the circle at T- - BTA-45- and - PTB-70- Find - ABT-In fig ii O is the centre and PQ is a tangent to circle at R- Calculate - STR-

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Two figures a...

Question

Two figures are given
In fig (i) $P Q$ is a tangent to the circle at $T, ∠ B T A = 45^{\circ} a n d ∠ P T B = 70^{\circ}$ . Find $∠ A B T$ .
In fig (ii) $O$ is the centre and $P Q$ is a tangent to circle at $R$ . Calculate $∠ S T R$ .

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Solution

$I n F i g u r e 1 ∠ B T A = 45 (G i v e n) ∠ P T B = 70 (G i v e n) ∠ A T P = ∠ P T B + ∠ B T A = 45 + 70 = 115...... (1) ∠ A T Q + ∠ A T P = 180 (L i n e a r P a i r o f a n g l e s) ∠ A T Q = 180 - ∠ A T P = 180 - 115 = 65 [F r o m (1)] ∴ ∠ A B T = ∠ A T Q = 65 [A n a n g l e b e t w e e n a t a n g e n t a n d a c h o r d t h r o u g h t h e p o i n t o f c o n t a c t i s e q u a l t o t h e a n g l e i n t h e a l t e r n a t e s e g m e n t] . I n F i g u r e 2 ∠ T R Q = 30 (G i v e n) ∠ S R T = 90 [A n g l e i n a s e m i c i r c l e] N o w ∠ R S T = ∠ T R Q = 30 [A n g l e s i n t h e a l t e r n a t e s e g m e n t s] ∴ ∠ R T S = 90 - 30 = 60$

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Two figures are givenIn fig (i) PQ is a tangent to the circle at T,∠BTA=45∘and∠PTB=70∘. Find ∠ABT.In fig (ii) O is the centre and PQ is a tangent to circle at R. Calculate ∠STR.

Two figures are given
In fig (i) $P Q$ is a tangent to the circle at $T, ∠ B T A = 45^{\circ} a n d ∠ P T B = 70^{\circ}$ . Find $∠ A B T$ .
In fig (ii) $O$ is the centre and $P Q$ is a tangent to circle at $R$ . Calculate $∠ S T R$ .