Question

in figure the circle s with centers p and qtouch each otherat r a line passing through r meet s the circle at a and b respectively​

Answer 1

Answer:

Refer image,

Given: Two circles with centres P and Q touch each other at R. A line passing through R meets the circles at A and B respectively.

To prove:

(i) segAP∣∣segBQ

(ii) ΔAPR∼ΔRQB

(iii) Finding ∠RQB if ∠PAR=35

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Solution:

(i) Radii of the same circle are equal.

∴PA=PR and RQ=BQ

∴∠PAR=∠PRA and ∠BRQ=∠RBQ

Also, ∠PRA=∠BRQ (vertically opposite angles)

∴∠PAR=∠RBQ

∴AP∣∣BQ (proved)

(ii) ∠PAR=∠RBQ

∠PRA=∠RBQ

∴∠APR=∠RQB

∴ΔAPR∼ΔRQB (proved)

(iii) ∠PAR=35

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∴∠RBQ=35

0

∴BRQ=35

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(∵BQ=RQ)

In triangle RBQ,

35

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+35

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+∠RQB=180

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or, ∠RQB=180

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−70

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∴∠RQB=110

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Step-by-step explanation:

hope it maybe helpful for you