Question

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ABCD is a cyclic quadrilateral. AB = AD. PAQ is a tangent to the circle. BA is produced to a point T. Angle DAT = 112 degree. FInd angle PAD and AOB
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Answer 1

Answer:

Join OC,OD and AC

(i)

∠BCG+∠BCD=180° [Linear pair]

⇒108° +∠BCD=180°

⇒∠BCD=180° −108° =72°

BC=CD

∴∠DCP=∠BCT

But,∠BCT+∠BCD+∠DCP=180°

∴∠BCT+∠BCT+72° =180°

2∠BCT=180° −72°

∠BCT=54°

(ii)

PCT is tangent and CA is a chord

∠CAD=∠BCT=54°

But arc DC subtends ∠DOC at the centre and ∠CAD at the remaining part of the circle.

∴∠DOC=2∠CAD=2×54°

o

=108°

Step-by-step explanation:

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