Home
Class 14
MATHS
The tangent at a point A of a circle wit...

The tangent at a point A of a circle with centre O intersects the diameter PQ of the circle (when extended) at the point B. If `angle BAP = 125^(@)`, then `angleAQP` is equal to :

A

`45^(@)`

B

`55^(@)`

C

`60^(@)`

D

`50^(@)`

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we need to find the value of angle AQP given that angle BAP is 125°. ### Step-by-Step Solution: 1. **Understanding the Geometry**: - We have a circle with center O and a diameter PQ. - A tangent at point A intersects the extended diameter PQ at point B. - We know that angle BAP = 125°. 2. **Using the Tangent-Secant Theorem**: - According to the properties of tangents and chords, the angle between the tangent (BA) and the chord (AP) is equal to the angle subtended by the chord (AP) on the opposite side of the tangent. - Therefore, angle BAP = angle AQP. 3. **Finding angle AQP**: - Since angle BAP = 125°, we can conclude that angle AQP also equals 125°. 4. **Final Answer**: - Thus, angle AQP = 125°.
Promotional Banner

Similar Questions

Explore conceptually related problems

The tangent at a point A of a circle with centre O intersects the diameter PQ of the circle (when extended) at the point B. If angle BAP = 125^@ , then angle AQP is equal to: केंद्र O के साथ एक वृत्त के बिंदु A पर स्पश्रेखा, बिंदु , B पर वृत्त के व्यास PQ ( जब विस्तारित) को काटती है यदि angle BAP = 125^@ है, तो angle AQP के ज्ञात करें ।

The tangent at a point A on a circle with center O intersects the diameter PQ of the circle, when extended,at point B. If angleBAQ=105^(@) , then angleAPQ is equal to:

In figure PQ is tangent to the circle with centre at O at the point B , if angle AOB = 100^(@) , then angle ABP is equal to

In figure-3, PQ is tangent to the circle with centre at O, at the point B. if angleAOB=100^(@) , then angleABP is equal to

PQ is tangent at a point R of the circle with centre O. If ST is a diameter of the circle and angle TRQ = 30^(@) find angle PRS

PA and PB are tangents to a circle with centre 0, from a point P outside the circle, and A and B are point on the circle. If angleAPB = 30^(@) , then angleOAB is equal to:

PA and PB are two tangents to a circle with centre O, from a point P outside the circle. A and B are points on the circle. If angleAPB =100^(@) , then OAB is equal to:

PA and PB are two tangents to a circle with centre 0. from a point P outside the circle. A and B are points on the circle. If angleAPB= 70^@ then angleOAB is equal to:

The tangents at two points A and B on the circle with centre O intersect at P. If in quadrilateral PAOB, angle AOB : angle APB = 5 : 1 , then measure of angle APB is :

In the given figure, PQ is a tangent at a point R of the circle with centre O. If angle TRQ = 30^(@) , then angle PRS is equal to