ICSE Class 10CISCE
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In the Given Figure, O is the Centre of the Circle. the Tangents at B and D Intersect Each Other at Point P. If Ab is Parallel to Cd and ∠Abc = 55°, Find: (I) ∠Bod (Ii) ∠Bpd - ICSE Class 10 - Mathematics

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Question

In the given figure, O is the centre of the circle. The tangents at B and D intersect each other at point P. If AB is parallel to CD and ∠ABC = 55°, find:

(i) ∠BOD (ii) ∠BPD

Solution

i)
`∠`BOD = 2 `∠`BCD
⇒  `∠`BOD =  2 × 55° =  110°
ii) Since, BPDO is cyclic quadrilateral, opposite angles are supplementary.
∴ `∠`BOD  + `∠`BPD  = 180°
⇒  `∠`BPD =  180° -  110° =  70°

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Solution In the Given Figure, O is the Centre of the Circle. the Tangents at B and D Intersect Each Other at Point P. If Ab is Parallel to Cd and ∠Abc = 55°, Find: (I) ∠Bod (Ii) ∠Bpd Concept: Cyclic Properties.
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