Go To Your Study Dashboard

Get Answers to all your Questions

header-bg

In Fig. 1, O is the centre of the circle, PQ is a chord and PT is tangent to the circle at P. If $\angle P\!O\!Q=70^{\circ}$ , find $\angle T\!PQ$ .

Answers (1)

Given : PT is tangent.

$\angle POQ=70^{\circ}$

To find : $\angle TPQ$

In $\bigtriangleup POQ$ ,

$PO=OQ$ (Radius of the circle)

$\Rightarrow \angle OPQ = \angle OQP$ (equal sides have equal angles)

$\Rightarrow \angle OPQ + \angle OQP + \angle POQ =180^{\circ}$ (sum of angles of a triangle)

$\Rightarrow \angle OPQ + \angle OQP + 70^{\circ} =180^{\circ}$

$\Rightarrow 2\angle OPQ =180^{\circ} - 70^{\circ}$

$\Rightarrow 2\angle OPQ =110^{\circ}$

$\Rightarrow \angle OPQ =\frac{110^{\circ}}{2}=55^{\circ}$

Now $\angle OPT =90^{\circ}$ (tangent and radius make a right angle at point of contact)

$\Rightarrow \angle OPT = \angle OPQ + \angle T\!PQ =90^{\circ}$

$\Rightarrow 55^{\circ} + \angle T\!PQ =90^{\circ}$

$\Rightarrow \angle T\!PQ =90^{\circ}-55^{\circ}$

$\Rightarrow \angle T\!PQ =35^{\circ}$

Posted by

Safeer PP

View full answer

Similar Questions

Trending Articles/News

anam-khan

CBSE Board Class 10 Result LIVE: When are CBSE 10th results coming to results.cbse.nic.in? 2nd exams schedule

anam-khan

CBSE changing Class 9, 10 syllabus from 2026-27; 3rd language compulsory, 2 levels of maths, science

anam-khan

CBSE AI Curriculum for Classes 3-8: What’s in the syllabus, how will it be taught, will there be exams?

Latest Question